2. EJE : NÚMEROS
Photo
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● Happy teacher helping her students
4. OBJETIVO DE APRENDIZAJE
Identificar los conjuntos numéricos y sus características.
Comprender los conjuntos numéricos en términos de los problemas
asociados a ellos.
Reconocer las propiedades de los números reales.
13. Determinar el m.c.m. entre 3, 4 y 8.
1. Múltiplos positivos de 3 ={3, 6, 9, 12, 15, 18, 21, 24, 27….}
2. Múltiplos positivos de 4 ={4, 8, 12, 16, 20, 24, 28, 32…}
3. Múltiplos positivos de 8 ={8, 16, 24, 32, 40, …}
El m.c.m. entre 3, 4 y 8 es 24. (Dentro de los múltiplos positivos que
tienen en común, 24 es el menor)
MÍNIMO COMÚN MÚLTIPLO (M.C.M.)
14. El m.c.m. también se puede obtener a través del siguiente método:
Solo utilizando números primos, se divide cada número hasta que en
cada columna resulte 1. Luego, el producto entre los números primos
usados corresponde al m.c.m.
Determinar el m.c.m. entre 3, 4 y 8.
m.c.m. = 23 · 3 = 24
MÍNIMO COMÚN MÚLTIPLO (M.C.M.)
3 4 8 2
3 2 4 2
3 1 2 2
3 1 1 3
1
16. Determinar el M.C.D. entre 14, 56 y 98.
1. Divisores positivos de 14 ={1, 2, 7,14}
2. Divisores positivos de 56 ={1, 2, 4, 7, 8, 14, 28, 56}
3. Divisores positivos de 98 ={1, 2, 7, 14, 49, 98}
El M.C.D. entre 14, 56 y 98 es 14. (Dentro de los divisores positivos que
tienen en común, 14 es el mayor)
MÁXIMO COMÚN DIVISOR (M.C.D.)
17. El M.C.D. también se puede obtener a través del siguiente método:
Solo se utilizan números primos que sean divisores simultáneos de
los números. Cuando ya no se puedan dividir todos, finaliza el
método. El producto de los primos usados es el M.C.D.
Determinar el M.C.D. entre 14, 56 y 98.
M.C.D. = 2 ∙ 7 = 14
MÁXIMO COMÚN DIVISOR (M.C.D.)
14 56 98 2
7 28 49 7
1 4 7
18. 1. El M.C.D. de 64, 32 y 24 es
A) 2
B) 4
C) 8
D) 16
E) 24
19. 1. El M.C.D. de 64, 32 y 24 es
A) 2
B) 4
C) 8
D) 16
E) 24
Habilidad: Aplicación
C
Luego el M.C.D. = 2 ∙ 2 ∙ 2 = 8
20. 2. ¿Cuál de los siguientes números NO es un racional?
40. Decimal
Finito
Infinito
Semiperiódico
Infinito
Periódico
Tienen una cantidad finita de
numeros decimales
Despues de la coma hay una o
mas cifras que se repiten
indefinidamente.
En los cuales no todas las cifras
de la parte decimal se repiten.
La parte decimal que no se
repite se llama anteperíodo, y
la parte decimal que se repite
corresponde al período.
NUMEROS RACIONALES DECIMALES
41. Clasifica cada número decimal en finito, infinito periódico o infinito
semiperiódico.
ACTIVIDAD 2
42. CONVERSIÓN DE NUMEROS DECIMALES A FRACCIÓN.
En la fracción que lo representa:
• El numerador corresponde a todo el número decimal sin
la coma.
• El denominador, al valor de una potencia de base 10 con
tantos ceros como cifras tenga la parte decimal del
número.
43. CONVERSIÓN DE NUMEROS DECIMALES A FRACCIÓN.
En la fracción que lo representa:
• En el numerador se calcula la diferencia entre el número
decimal sin la coma y la parte entera.
• En el denominador se escriben tantos 9 como cifras
tenga el período.
44. CONVERSIÓN DE NUMEROS DECIMALES A FRACCIÓN.
En la fracción que lo representa:
• En el numerador se escribe la diferencia entre el número
decimal sin la coma y el número que aparece antes del
período
• En el denominador se escriben tantos 9 como cifras tenga el
período y tantos 0 como cifras tenga el ante período.
46. Adición y sustraccion de fracciones
Para sumar o restar fracciones estas tienen que tener el mismo
denominador.
a) Si el denominador es igual, solo operamos los numeradores y
mantenemos el denominador.
Ejemplos
47. Adición y sustraccion de fracciones
Para sumar o restar fracciones estas tienen que tener el mismo
denominador.
b) Si el denominador es distinto, obtenemos el mcm y multiplicamos
cada fracción por el número que le corresponde. Luego,se reducen
los denominadores a un común denominador y se suman o restan los
numeradores de las fracciones equivalentes obtenidas.
Ejemplos
48. Multiplicación entre Fracciones
Es decir, si a, b, c, d ∈ ℤ, entonces
Al multiplicar dos fracciones resulta otra fracción cuyo numerador
es el producto de los numeradores de los factores y cuyo
denominador es el producto de los denominadores.
Ejemplo
2 ∶ 2
12: 2
=
1
6
Simplificamos por 2
49. División entre Fracciones
Es decir, si a, b, c, d ∈ ℤ,
entonces
Se debe invertir la SEGUNDA FRACCIÓN, es decir, cambiar el
denominador por el numerador y cambiar el numerador por el
denominador. Después, se multiplican las dos fracciones.
Ejemplo
55. EL CONJUNTO DE LOS NUMEROS RACIONALES
Al multiplicar dos fracciones resulta otra fracción cuyo numerador es el producto de los
numeradores de los factores y cuyo denominador es el producto de los denominadores, es
decir, si a, b, c, d ∈ N, entonces
57. WHOA!
This could be the part of the
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introduce yourself, write your email…
58. “This is a quote, words full of wisdom that
someone important said and can make
the reader get inspired.”
—SOMEONE FAMOUS
59. Venus Mercury Mars
Mercury is the closest
planet to the Sun and the
smallest of them all
Despite being red, Mars is
a cold place. The planet is
full of iron oxide dust
en la fracción que lo
representa, el numerador
corresponde a todo el
número decimal sin la
coma, y el denominador,
al valor de una potencia
de base 10 con tantos
ceros como cifras tenga la
parte decimal del número
Study Objectives
60. Introduction
This could be the part of the presentation where
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61. Contents of This Template
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5. Instructions for use.
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62. “The closest planet to the Sun
and the smallest one in the
Solar System”
Literature Review
—Lisa Jane —Angelina Jones
“Venus has a beautiful name
and is the second planet from
the Sun. It’s terribly hot”
64. Methodology
Data study Comparison
Research Analysis
Saturn is a gas giant
and has rings
It’s a gas giant and
the biggest planet
It’s the closest planet
to the Sun
Venus is the second
planet from the Sun
02
01
03 04
65. Mercury is the closest
planet to the Sun and
the smallest of them all
Venus has a beautiful
name and is the second
planet from the Sun
Despite being red, Mars
is a cold place full of
iron oxide dust
Training scope
Teaching methods Teaching skills
Teacher Profile in Remote Education
66. Mercury is the closest
planet to the Sun
Venus has a beautiful
name, but it’s hot
Despite being red, Mars is
a cold place
Saturn is the ringed one
and a gas giant
Teaching Functions and Tasks
Technological Motivational
Academic Pedagogical
69. Rol Functions Students Training
Adviser 1 Academic 20-25 Disciplinary
Adviser 2 Pedagogical 20-25 Education Distance
Adviser 3 Technological 20-25 ICT
Multifunctional Model
70. Rol Functions Number of students Type of training
Adviser Academic and pedagogical 20-25
Discipline, Distance
Education and ICT
Tutor
Technological, motivational,
organizational and
administrative
40-55
Distance Education
and ICT
Bifunctional Model
71. Task Analysis
Programming 15,0% Students
15,0%
Age
5,0%
Language
15,0%
Platform
5,0%
Assigned 45,0%
To modify this graph, click on it, follow the link, change the data and paste the new graph here
72. Mercury is the closest
planet to the Sun
Despite being red, Mars is
a cold place
It’s the biggest planet in
the Solar System
Neptune is the farthest
planet from the Sun
Venus has a beautiful
name, but it’s hot
Saturn is the ringed one
and a gas giant
Validation of Tutoring Models
Administrative tasks Organizational tasks
Advisor information Tasks by role
Motivational tasks
Data of the courses
73. You Can Use a Table
Value Value
Mercury & Mars Earth
● The third from the Sun
● It harbors life
● It’s where we live on
● 110
● 100
● 333
● 029
● 200
● 080
Saturn
● It has several rings
● It’s a gas giant
● 018
● 382
● 003
● 033
74. Mars is the fourth planet from the
Sun and the second-smallest
planet in the Solar System, being
only larger than Mercury.
To modify this graph, click on it, follow the link, change the data and paste the new graph here
Online Teaching
Mars
Society Health Language Technology Computing
0
10
20
30
40
50
75. Planet Venus has a
beautiful name
Canada
Greater Use of Distance Education
It’s a gas giant and
the biggest planet
Russia
Despite being red,
Mars is a cold place
Chile
It’s composed of
hydrogen and helium
Australia
It’s the closest planet
to the Sun
South Africa
20%
15%
10%
35%
20%
76. A Timeline Always Works Well
Distance learning was
first invented
1895
Internet becomes a
household name
1989
Computer assisted
learning center
1982
3,5 million students
using E-learning
2006
77. Students enrolled in courses at degree-granting
postsecondary institutions in 2017
19.7 M
78. Students took at least one but
not all of their courses online
Students enrolled in exclusively
distance education
Students took more than half
of their courses online
3,2M (19,5%)
2,2M (13,3%) 274,211 (9,1%)
79. Course Start-development Tasks
Despite being
red, it’s a very
cold place
Mars
02
It’s the biggest
planet in the
Solar System
Jupiter
03
Mercury
04
Mercury is the
closest planet
to the Sun
It’s the second
planet from
the Sun
Venus
01
80. Helena Patterson
Anton Smith
John Doe
You can replace the star
on the screen with a
picture of this person You can replace the star
on the screen with a
picture of this person
You can replace the star
on the screen with a
picture of this person
Our Team
81. Conclusions
The closest planet to the Sun and the
smallest one in the Solar System—it’s
only a bit larger than the Moon
1
It’s terribly hot—even hotter than
Mercury—and its atmosphere is
extremely poisonous
2
82. ● AUTHOR (YEAR). Title of the publication. Publisher
● AUTHOR (YEAR). Title of the publication. Publisher
● AUTHOR (YEAR). Title of the publication. Publisher
● AUTHOR (YEAR). Title of the publication. Publisher
● AUTHOR (YEAR). Title of the publication. Publisher
Bibliographical References
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